A Cognitive Typology for Numerical Notation

Cambridge Archaeological Journal • Vol/Iss. 14(1) • McDonald Institute for Archaeological Research • Cambridge UK • Published In • Pages: 37-52 •
By Chrisomalis, Stephen

Abstract

In this article, the author suggests a new topology of numerical notation systems. This new typology organizes each system by two axes. The first of these axes is cumulative versus ciphered versus multiplicative and the other is additive versus positional. The author goes on to argue that, considering the intelligibility of number systems even in the absence of knowledge about their associated language, human number systems are a reflection of cognitive processes. Finally, the author uses this new typology to build a theoretical model of numerical system evolution over time. The article concludes with suggestions for utilizing this typology in future cross-cultural research.

Note

This paper considers a cross-cultural sample of numerical systems and, while it does not test hypotheses per se, it does provide a number of explanatory observations based on the data from the sample. These observations are listed below.

Samples

Sample Used Coded Data Comment
Unique sample of 17 numerical notation systemsresearcher's own

Hypotheses (5)

HypothesisSupported
"Additive systems do not develop from positional ancestors" (p. 46)Support claimed
"Cumulative systems do not develop from non-cumulative ancestors" (p. 46)Support claimed
Over time there is an increase in non-cumulative over cumulative systems and of positional over non-positional systems (p. 47)Support claimed
"Positional systems are not replaced by additive systems" (p. 47)Support claimed
"Non-cumulative systems are not replaced by cumulative systems" (p. 48)Support claimed
Documents and Hypotheses Filed By: dmccloskey103  anj.droe